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Andy Puzder didn’t pay taxes for an undocumented worker he employed as housekeeper for several years until after President Donald Trump nominated him for labor secretary, a spokesman for the fast-food executive said Tuesday.

The “taxes were paid recently, since the nomination,” said George Thompson, spokesman for Mr. Puzder.

Mr. Puzder wasn’t aware of the housekeeper’s immigration status during the four to five years she worked for his family. The woman was terminated after Mr. Puzder discovered she was an illegal immigrant, and offered assistance in obtaining legal status.

“Andy admitted the mistake and has paid all related taxes,” Mr. Thompson said. “He has taken all available steps to remediate it.”

The spokesman clarified Tuesday taxes were only paid after Mr. Trump made his pick in early December. The employment of the housekeeper and a related tax issue were disclosed Monday. The housekeeper worked part time for the Puzder household.

The status of Mr. Puzder’s former housekeeper further complicates his slow-moving confirmation process. The Labor Department oversees how U.S. labor laws, including wage-and-hour rules, apply to immigrant workers.